Coordination Requires Simplification: Thermodynamic Bounds on Multi-Objective Compromise in Natural and Artificial Intelligence (2509.23144v3)

Abstract: Information-processing systems that coordinate multiple agents and objectives face fundamental thermodynamic constraints. We show that solutions with maximum utility to act as coordination focal points have a much higher selection pressure for being findable across agents rather than accuracy. We derive that the information-theoretic minimum description length of coordination protocols to precision $\varepsilon$ scales as $L(P)\geq NK\log_2 K+N^2d^2\log (1/\varepsilon)$ for $N$ agents with $d$ potentially conflicting objectives and internal model complexity $K$. This scaling forces progressive simplification, with coordination dynamics changing the environment itself and shifting optimization across hierarchical levels. Moving from established focal points requires re-coordination, creating persistent metastable states and hysteresis until significant environmental shifts trigger phase transitions through spontaneous symmetry breaking. We operationally define coordination temperature to predict critical phenomena and estimate coordination work costs, identifying measurable signatures across systems from neural networks to restaurant bills to bureaucracies. Extending the topological version of Arrow's theorem on the impossibility of consistent preference aggregation, we find it recursively binds whenever preferences are combined. This potentially explains the indefinite cycling in multi-objective gradient descent and alignment faking in LLMs trained with reinforcement learning with human feedback. We term this framework Thermodynamic Coordination Theory (TCT), which demonstrates that coordination requires radical information loss.

• The paper establishes that coordination protocols require simplification due to exponential scaling of precision costs with increasing agents and conflicting objectives.
• It introduces Thermodynamic Coordination Theory (TCT), deriving minimum description lengths from information theory to quantify coordination limits.
• Empirical insights link TCT to phenomena in AI and organizational systems, emphasizing simplified coordination as key to achieving resilience.

Coordination Requires Simplification: Thermodynamic Bounds on Multi-Objective Compromise in Natural and Artificial Intelligence

Introduction

This paper explores the thermodynamic constraints faced by complex information-processing systems that attempt multi-agent coordination across conflicting objectives. By establishing fundamental scaling laws, the research posits that coordination requires radical simplification due to inherent information-theoretic pressures. These pressures necessitate compromising the precision of coordination protocols, which influences emergent systemic behaviors. The study introduces the Thermodynamic Coordination Theory (TCT), emphasizing the need for information simplification as multiple agents converge on coordination solutions within finite operational limits.

Thermodynamic Bounds on Coordination Protocols

The paper derives the minimum description length of coordination protocols using principles from information theory. The key result states:

$L(P) \geq NK\log_2 K+N^2d^2\log (1/\varepsilon)$

where $N$ is the number of agents, $d$ is the dimensionality of potentially conflicting objectives, $K$ is the internal model complexity, and $\varepsilon$ denotes coordination precision. This indicates that achieving precision in coordination scales super-linearly with the number of agents and objectives, resulting in a significant requirement for information simplification.

The analysis further explores hierarchical coordination, suggesting that subgroups or factions bring down communication costs but still face progressive information loss at each level. This provides an underpinning structure for understanding the hierarchical organization in complex systems such as LLMs and organizational management models.

Findability versus Accuracy

In multi-agent systems, selection pressure toward 'findability' of solutions (utility) surpasses pressure for accuracy. The paper establishes that the probability of an agent identifying and choosing a suitable solution reduces exponentially with system size, thus indicating a larger attraction towards solutions that are simpler yet broadly acceptable over precise but complex alternatives. This can lead to emergent metastable states as agents form consensus around easily coordinatable Schelling points, both in natural and artificial contexts.

Phase Transitions and Coordination Temperature

The research describes 'coordination temperature' $T_{\rm co}$ as a metric for system disorder analogous to thermal systems. As $T_{\rm co}$ increases, systems gravitate towards simplified coordination focal points due to excessive disorder (variance in agent models).

The paper predicts phase transitions in coordination dynamics at critical coordination temperatures, which are conceptualized as points where systems transition to significantly simplified modes. This ties back to empirical observations in reinforcement learning, where systems trained with human feedback cycle indefinitely without convergence.

Empirical Implications and Applications

The implications of TCT are multidimensional and cross-domain. In AI, observed indefinite cycling in multi-objective gradient descent processes supports the theoretical foundations of TCT. Analogously, bureaucracies, social systems, and market dynamics exhibit similar patterns of resilience and breakdown due to these coordination constraints. The framework provides insights into designing more sustainable and resilient systems by managing information complexity holistically and accepting the inherent need for systemic simplifications at scale.

Conclusion

"Coordination Requires Simplification: Thermodynamic Bounds on Multi-Objective Compromise in Natural and Artificial Intelligence" presents a theoretical framework which combines thermodynamics, information theory, and social choice theory. It asserts fundamental constraints on coordination in complex systems, propelling the need for simplification and providing a lens to evaluate diverse systems across scales and domains. As multi-agent systems continue to integrate into modernity, understanding and applying these findings can enhance AI robustness, organizational resilience, and policy-making efficiency. Future directions include empirical verification of proposed scaling laws and application of TCT concepts within specific machine learning architectures to optimize design strategies and performance outcomes.

Figure 1: Thermodynamic Coordination Theory: Key Relationships.